Renormalization-group calculations for U(1)-symmetric spin systems and gauge theories

Journal Article · Sat Aug 15 04:00:00 EDT 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.24.941· OSTI ID:6336616

Hamber, H W

We present a real-space renormalization-group analysis for the U(1) spin model in two and three dimensions and for compact electrodynamics in three and four dimensions. The Hamiltonian formulation of the theory defined on a hypercubic spatial lattice is used. The nonperturbative renormalization-group transformations we derive give continuous phase transitions for the spin models, in two and three dimensions. In three dimensions the gap exponent agrees remarkably well with series-expansion results. For the gauge theory we find, in agreement with Polyakov, that compact electrodynamics in three dimensions confines for all values of the coupling constant. A calculation for the string tension shows that it vanishes with an essential singularity at zero coupling. In four dimensions for weak enough coupling confinement is lost and the theory shows a phase transition between a charge-confining and a free-photon phase.

• Research Organization: Department of Physics, University of California, Santa Barbara, California 93106
• OSTI ID: 6336616
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 24:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645302* -- High Energy Physics-- Particle Invariance Principles & Symmetries-- Applications to Electromagnetic & Weak Interactions-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
COUPLING CONSTANTS
ELECTRODYNAMICS
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
MECHANICS
PARTICLE PROPERTIES
QUANTUM OPERATORS
RENORMALIZATION
SPIN
STATISTICAL MECHANICS
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS